Tag selector like stackexchange?

you can do that using JQuery autocomplete plugin

and once you have included all of the needed JS files just add this code after your new post form

$terms = get_terms("post_tag");
$tags="";
$count = count($terms);
 if ( $count > 0 ){ 
     foreach ( $terms as $term ) {
       $tags .=  '"'.$term->name.'", '; 
    }
    $tags = substr($tags,0,-2);
 }

echo ' <script>
JQuery("#post_tags").autocomplete(['.$tags.'], {
        width: 320,
        max: 4,
        highlight: true,
        multiple: true,
        multipleSeparator: ", ",
        scroll: true,
        scrollHeight: 300
    });
</script>';

note: Now this is good if you only have a small number of tags, but if you have hundreds or thousands of tags then using an ajax solution is a must.